Unification Scale Research Articles

A twist on broken U(3) $$\times $$ U(3) supersymmetry

What symmetry breaking would be required for gauginos from a supersymmetric theory to behave like left-handed quarks of the Standard Model? Starting with a supersymmetric SU(3) $$\times $$ SU(3) $$\times $$ U(1) $$\times $$ U(1) gauge theory, the 18 adjoint-representation gauginos are replaced with 2 families of 9 gauginos in the (3,3*) representation of the group. After this explicit breaking of supersymmetry, two-loop quadratic divergences still cancel at a unification scale. Coupling constant unification is supported by deriving the theory from an SU(3) $$\times $$ SU(3) $$\times $$ SU(3) $$\times $$ SU(3) Grand Unified Theory (GUT). $${\hbox {Sin}}^2$$ of the Weinberg angle for the GUT is 1/4 rather than 3/8, leading to a lower unification scale than usually contemplated, $$\sim 10^9 \, \hbox {GeV}$$ . After spontaneous gauge symmetry breaking to SU(3) $$\times $$ SU(2) $$\times $$ U(1), the theory reproduces the main features of the Standard Model for two families of quarks and leptons, with gauginos playing the role of left-handed quarks and sleptons playing the role of the Higgs boson. An extension to the theory is sketched that incorporates the third family of quarks and leptons.

Gravitational misalignment mechanism of Dark Matter production

We consider Dark Matter composed of an oscillating singlet scalar field. On top of the mass term, the scalar is equipped with a potential spontaneously breaking Z2-symmetry. This potential dominates at early times and leads to the time-dependent expectation value of the scalar, which decreases in the expanding Universe. As it drops below some critical value, the symmetry gets restored, and the Dark Matter field starts to oscillate around zero. We arrange the spontaneous symmetry breaking through the interaction of the scalar with the Ricci curvature. In that way, superheavy Dark Matter can be produced at very early times. Depending on its mass, the production takes place at inflation (very large masses up to the Grand Unification scale), at preheating, or at radiation-dominated stage (masses 106−107 GeV).

Grand pleromal transmutation: UV condensates via Konishi anomaly, dimensional transmutation and ultraminimal GUTs

Using consistency requirements relating chiral condensates imposed by the so called Generalized Konishi Anomaly, we show that dimensional transmutation via gaugino condensation in the ultraviolet drives gauge symmetry breaking in a large class of asymptotically strong Super Yang Mills Higgs theories. For Adjoint multiplet type chiral superfields Φ (transforming as r×r¯ representations of a non Abelian gauge group G), solution of the Generalized Konishi Anomaly (GKA) equations allows calculation of quantum corrected VEVs in terms of the dimensional transmutation scale ΛUV≃MXe8π2g2(MX)b0 which determines the gaugino condensate. Thus the gauge coupling at the perturbative unification scale MX generates GUT symmetry breaking VEVs by non-perturbative dimensional transmutation. This obviates the need for large (or any) input mass scales in the superpotential. Rank reduction can be achieved by including pairs of chiral superfields transforming as either (Q(r),Q¯(r¯)) or (Σ((r⊗r)symm)),Σ‾((r¯⊗r¯)symm), that form trilinear matrix gauge invariants Q¯⋅Φ⋅Q,Σ‾⋅Φ⋅Σ with Φ. Novel, robust and ultraminimal Grand unification algorithms emerge from the analysis. We sketch the structure of a realistic Spin(10) model, with the 16-plet of Spin(10) as the base representation r, which mimics the realistic Minimal Supersymmetric GUT but contains even fewer free parameters. We argue that our results point to a large extension of the dominant and normative paradigms of Asymptotic Freedom/IR colour confinement and potential driven spontaneous symmetry breaking that have long ruled gauge theories.

Probing unification with precision Higgs physics

We propose a novel approach of probing grand unification through precise measurements on the Higgs Yukawa couplings at the LHC. This idea is well motivated by the appearance of effective operators not suppressed by the mass scale of unification ${M}_{\mathrm{U}}$ in realistic models of unification with the minimal structure of Yukawa sector. Such operators modify the Higgs Yukawa couplings in correlated patterns at scale ${M}_{\mathrm{U}}$ that hold up to higher-order corrections. The coherences reveal a feature that, the deviation of tau Yukawa coupling relative to its standard model value at the weak scale is the largest one among the third-generation Yukawa couplings. This feature, if verified by the future LHC, can serve as a hint of unification.

Relative scales of the GUT and twin sectors in an F-theory model

In this note we analyze the relative scales for the GUT and twin sectors in the F-theory model discussed in ref. [1]. There are a number of volume moduli in the model. The volume of the GUT surface in the visible sector (1) (with the Wilson line GUT breaking) defines the GUT scale MG∼ 2 × 1016GeV as the unification scale with precise gauge coupling unification of SU(3) × SU(2) × U(1)Y . We choose the GUT coupling constant, {alpha}_G^{-1} ∼ 24. We are then free to choose the ratio αG(2)/αG(1) = m1/m2 with m1 and m2 independent volume moduli associated with the directions perpendicular to the two asymptotic GUT surfaces. We then analyze the effective field theory of the twin sector (2), which may lead to a SUSY breaking gaugino condensate. Of course, all these results are subject to the self-consistent stabilization of the moduli.

Dynamical Higgs field alignment in the NMSSM

Experimental probes of the recently discovered Higgs boson show that its behavior is close to that of the Standard Model (SM) Higgs particle. Extensions of the SM which include extra Higgs bosons are constrained by these observations, implying either the decoupling of the heavy non-standard Higgs particles or the realization of alignment, associated with vanishing mixing of the SM-like Higgs boson with the non-standard ones. Quite generally, alignment is not enforced by symmetry considerations and hence it is interesting to look for dynamical ways in which this condition can be realized. We show that this is possible in the Next-to-Minimal Supersymmetric Standard Model (NMSSM), in which alignment is achieved for values of the coupling of the Higgs fields to the singlet field that become large close to the Grand Unification (GUT) scale. This, in turn, can be explained by the composite nature of the Higgs fields, with a compositeness scale close to the GUT scale. In this article we present this dynamical scenario and discuss its phenomenological properties.

Alternative renormalizable SO(10) GUTs and data fitting

The alternative renormalizable minimal SO(10) model is composed of the Yukawa couplings with 10⊕120 Higgs fields, whereas the right-handed (RH) neutrino Majorana masses are generated via the Witten mechanism. The gauge coupling unification is achieved together with a unique pattern of the fermion masses and mixing at the grand unification scale due to additional contributions of vector-like quarks to the standard model renormalization group equations. We perform the fitting of the model to the experimental data of charged fermion masses and the CKM matrix. The best fit point is obtained with large pulls for mc, ms, mb, and mτ. For the modifications to the minimal model by adding either 10′ or 120′, a large deviation for the tau mass rules out all these models. In the case with the bottom and vector-like quark mixing, the mass matrices are well fitted the charged fermions but the bound on the light neutrino mass scale excludes this scenario. To ameliorate this deficit, we consider the two-step symmetry breaking scenario, SO(10)→SU(5)→SU(3)C×SU(2)L×U(1)Y, with the SO(10) breaking at the Planck scale leading to the radiatively generated RH neutrino Majorana masses being at the ordinary seesaw scale. For this case, we find the best fit point with χ2=7.8 consistent with experimental results including the neutrino sector. The largest deviation is 2.3σ corresponding to the strange quark mass. Hence, a more precise determination of the strange quark mass can test this model. For the best fit point, we find the effective Majorana neutrino mass of mββ=0.22 meV and the sum of light neutrino masses as Σ=0.078 eV, which are consistent with the current constraints from the search for the neutrinoless double beta decay and the CMB anisotropy measurement.

Prospect of dark matter searches in split SUSY models

The results from the XENON1T/Panda-X and IceCube experiments have set severe upper limits on spin-independent (SI) and spin-dependent (SD) scattering cross section of weakly interacting massive particles on nuclei. In the framework of split supersymmetry scenario supported by the LHC constraints, we investigate the prospect of dark matter (DM) direct and indirect detection experiments. Assuming a relation among gaugino masses at the grand unification scale, we have specified the parameter regions that predict the right DM relic abundance as well as satisfy the constraints on SI and SD scattering cross sections of DM. In the case of universal gaugino masses, the XENON1T/Panda-X results have ruled out completely the well-tempered neutralino region. We have found that 200 times smaller than the current IceCube bound is the sensitivity limit that a future DM indirect detection experiment should have at least in order to have a certain impact beyond the current XENON1T/Panda-X results. The future results from XENON1T will be able to test a signification portion of the Higgsino-like region. Although there are points in the Higgsino-like region that cannot be reached by future DM detection experiments, direct production channels of neutralino/chargino can be used to test the model at the LHC/HL-HLC. In the case of non-universal gaugino masses, beside showing the allowed parameter space, we have specified the regions that can be tested at both future DM direct and indirect detection experiments. One of them are Higgsino-like region, while the others two predict a well mixed bino-wino DM. The DM properties in each region have been examined and demonstrated with a benchmark of-ino spectrum. Interestingly, points in the mixed bino-wino region with rather light chargino can be tested the LHC 14 TeV.

Trans-Planckian censorship and inflation in grand unified theories

The recently proposed trans-Planckian censorship conjecture (TCC) amounts to the claim that inflation models with an inflationary energy scale larger than Λinfmax∼109GeV belong to the swampland, i.e., cannot be embedded into a consistent theory of quantum gravity. In this paper, we point out that this constraint can be readily satisfied in D-term hybrid inflation (DHI), which is a well-motivated inflation scenario in the context of supersymmetric grand unification. In DHI, the amplitude of the primordial scalar power spectrum originates from a Fayet–Iliopoulos term of the order of the unification scale, ξ∼1016GeV. At the same time, the TCC results in an upper bound on the corresponding gauge coupling constant of gmax∼10−14. We are able to show that this constraint translates into an upper bound on the gravitino mass of m3/2max∼10MeV, which opens the possibility that dark matter is accounted for by thermally produced gravitinos, if the reheating temperature is close to Treh∼100TeV. Interestingly enough, a somewhat similar gravitino mass range has recently been derived in a model that aims at explaining dark energy in terms of axion quintessence and resolving the Hubble tension by means of decaying gravitino dark matter.

Testing the Seesaw Mechanism and Leptogenesis with Gravitational Waves.

We present the possibility that the seesaw mechanism with thermal leptogenesis can be tested using the stochastic gravitational background. Achieving neutrino masses consistent with atmospheric and solar neutrino data, while avoiding nonperturbative couplings, requires right handed neutrinos lighter than the typical scale of grand unification. This scale separation suggests a symmetry protecting the right-handed neutrinos from getting a mass. Thermal leptogenesis would then require that such a symmetry be broken below the reheating temperature. We enumerate all such possible symmetries consistent with these minimal assumptions and their corresponding defects, finding that in many cases, gravitational waves from the network of cosmic strings should be detectable. Estimating the predicted gravitational wave background, we find that future space-borne missions could probe the entire range relevant for thermal leptogenesis.

Triplet leptogenesis, type-II seesaw dominance, intrinsic dark matter, vacuum stability and proton decay in minimal SO(10) breakings

We implement type-II seesaw dominance for neutrino mass and baryogenesis through heavy scalar triplet leptogenesis in a class of minimal non-supersymmetric SO(10) models where matter parity as stabilising discrete symmetry as well as WIMP dark matter (DM) candidates are intrinsic predictions of the GUT symmetry. We also find modifications of relevant CP-asymmetry formulas in such models. Baryon asymmetry of the universe as solutions of Boltzmann equations is further shown to be realized for both normal and inverted mass orderings in concordance with cosmological bound and best fit values of the neutrino oscillation data including θ23 in the second octant and large values of leptonic Dirac CP-phases. Type-II seesaw dominance is at first successfully implemented in two cases of spontaneous SO(10) breakings through SU(5) route where the presence of only one non-standard Higgs scalar of intermediate mass ∼ 109−1010 GeV achieves unification. Lower values of the SU(5) unification scales ∼ 1015 GeV are predicted to bring proton lifetimes to the accessible ranges of Super-Kamiokande and Hyper-Kamiokande experiments. Our prediction of WIMP DM relic density in each model is due to a ∼ \U0001d4aa (1) TeV mass matter-parity odd real scalar singlet (⊂ 16H ⊂ SO(10)) verifiable by LUX and XENON1T experiments. This DM is also noted to resolve the vacuum stability issue of the standard scalar potential. When applied to the unification framework of M. Frigerio and T. Hambye, in addition to the minimal fermionic triplet DM solution of 2.7 TeV, our mechanism of type-II seesaw dominance and triplet leptogenesis is also found to make an alternative prediction of the triplet fermion plus the real scalar singlet DM near the TeV scale.

The QCD axion and unification

The QCD axion is one of the most appealing candidates for the dark matter in the Universe. In this article, we discuss the possibility to predict the axion mass in the context of a simple renormalizable grand unified theory where the Peccei-Quinn scale is determined by the unification scale. In this framework, the axion mass is predicted to be in the range ma ≃ (3–13) × 10−9 eV. We study the axion phenomenology and find that the ABRACADABRA and CASPEr-Electric experiments will be able to fully probe this mass window.

Cosmic microwave background dipole asymmetry could be explained by axion monodromy cosmic strings

Observations by the Wilkinson Microwave Anisotropy Probe and the Planck mission suggest a hemispherical power amplitude asymmetry in the cosmic microwave background, with a correlation length on the order of the size of the observable Universe. We find that this anomaly can be naturally explained by an axion-like particle (ALP) cosmic string formed near our visible Universe. The field variation associated to this cosmic string creates particle density fluctuations after inflation, which consequently decay into radiation before the Big Bang Nucleosynthesis (BBN) era and resulted in the observed power asymmetry. We find in this scenario that the hemispherical power amplitude asymmetry is strongly scale dependent: $A(k)\propto {\rm exp}(-kl)/k$. Admittedly, typical inflation models predict a relic number density of topological defects of order one per observable Universe and so in our model the cosmic string must be tuned to have an impact factor of order $1/H_0$. Interestingly, the constraints based on purely cosmological considerations also give rise to a Peccei-Quinn scale $F_a$ of order $10^3$ larger then the Hubble scale of inflation $H_I$. Assuming $H_I\sim 10^{13}$GeV, we then have an ALP with $F_a\sim 10^{16}$GeV, which coincides with the presumed scale of grand unification. As we require ALP decays occur before the BBN era, which implies a relatively heavy mass or strong self-coupling, and considering that the associated potential should break the shift symmetry softly in order to protect the system from radiative corrections, we also conclude that the required ALP potential should be monodromic in nature.

Light majoron cold dark matter from topological defects and the formation of boson stars

We show that for a relatively light majoron (≪ 100 eV) non-thermal production from topological defects is an efficient production mechanism. Taking the type I seesaw as benchmark scheme, we estimate the primordial majoron abundance and determine the required parameter choices where it can account for the observed cosmological dark matter. The latter is consistent with the scale of unification. Possible direct detection of light majorons with future experiments such as PTOLEMY and the formation of boson stars from the majoron dark matter are also discussed.

Natural Z′ -portal Majorana dark matter in alternative U(1) extended standard model

We consider a non-exotic gauged U(1)$_X$ extension of the Standard Model (SM), where the U(1)$_X$ charge of a SM field is given by a linear combination of its hypercharge and Baryon-minus-Lepton ($B-L$) number. All the gauge and mixed gauge-gravitational anomalies are cancelled in this model with the introduction of three right-handed neutrinos (RHNs). Unlike the conventional minimal U(1)$_X$ model, where a universal U(1)$_X$ charge of $-1$ is assigned to three RHNs, we consider an alternative charge assignment, namely, two RHNs ($N_R^{1,2}$) have U(1)$_X$ charge $-4$ while one RHN ($N_R$) has a $+5$ charge. With a minimal extension of the Higgs sector, the three RHNs acquire their Majorana masses associated with U(1)$_X$ symmetry breaking. While $N_R^{1,2}$ have Yukawa coupling with the SM lepton doublets and play an essential role for the 'minimal seesaw' mechanism, $N_R$ is isolated from the SM particles due to its U(1)$_X$ charge and hence it is a natural candidate for the dark matter (DM) without invoking additional symmetries. In this model context, we investigate the $Z^\prime$-portal RHN DM scenario, where the RHN DM communicates with the SM particles through the U(1)$_X$ gauge boson ($Z^\prime$ boson). We identify a narrow parameter space by combining the constraints from the observed DM relic abundance, the results of the search for a $Z^\prime$ boson resonance at the Large Hadron Collider Run-2, and the gauge coupling perturbativity up to the Planck/Grand Unification scale. For a special choice of U(1)$_X$ charges for the SM fields allows us to extend the model to SU(5)$\times$U(1)$_X$ grand unification. In this scenario, the model parameter space is more severely constrained, which will be explored at future high energy collider experiments.

New physics signature in D^0 (bar{D}^0)rightarrow f effective width asymmetries

Violation of charge conjugation-parity (mathrm CP) symmetry plays a major rule in the dominance of matter in our universe. A kind of mathrm CP violation results from the asymmetry of the life time measured in M^0 and {bar{M}}^0, here M is a heavy meson, decays to final states which is referred in the literature as A_{Gamma }^f. In this paper, we give an estimation of the upper bound on |A_{Gamma }^f| for the Cabibbo Favored D^0 rightarrow K^- pi ^+ decay process in different models. We show that in the standard model, |A_{Gamma }^f| lesssim {mathcal {O}} (10^{-10}). Recently a bound on A_{Gamma }^f has been obtained: (A^f_{Gamma })^{Exp.}= (1.6 pm 1)times 10^{-4}. This result motivates further studies on A_{Gamma }^f in beyond standard model physics. In the framework of two Higgs doublet model with generic Yukawa structure, we show that |A_Gamma ^{f}|lesssim {mathcal {O}} (10^{-7}) which is several orders of magnitude smaller than the current experimental value. Finally, in the framework of left-right symmetric models in which the mixing between the left and the right gauge bosons is allowed and the left-right symmetry is not manifest at unification scale, we find that A_{Gamma }^f can be as large as |A_{Gamma }^f|lesssim {mathcal {O}} (10^{-5}) which is one order of magnitude smaller than the experimentally measured value by LHCb collaborators.

Quartic coupling unification in the maximally symmetric 2HDM

We consider the Maximally Symmetric Two-Higgs Doublet Model (MS-2HDM) in which the so-called Standard Model (SM) alignment can be naturally realised as a consequence of an accidental SO(5) symmetry in the Higgs sector. This symmetry is broken (i) explicitly by renormalization-group (RG) effects and (ii) softly by the bilinear scalar mass term $m^2_{12}$. We find that in the MS-2HDM all quartic couplings can unify at large RG scales $\mu_X \sim 10^{11}\,$-$\,10^{20}$ GeV. In particular, we show that quartic coupling unification can take place in two different conformally invariant points, where all quartic couplings vanish. We perform a vacuum stability analysis of the model in order to ensure that the electro-weak vacuum is sufficiently long-lived. The MS-2HDM is a minimal and very predictive extension of the SM governed by only three additional parameters: the unification scale $\mu_X$, the charged Higgs mass $M_{h^{\pm}}$ (or $m^2_{12}$) and $\tan\beta$, which allow one to determine the entire Higgs sector of the model. In terms of these input parameters, we present illustrative predictions of misalignment for the SM-like Higgs-boson couplings to the $W^\pm$ and $Z$ bosons and, for the first time, to the top and bottom quarks.

A minimal SU(5) SuperGUT in pure gravity mediation

The lack of evidence for low-scale supersymmetry suggests that the scale of supersymmetry breaking may be higher than originally anticipated. However, there remain many motivations for supersymmetry including gauge coupling unification and a stable dark matter candidate. Models like pure gravity mediation (PGM) evade LHC searches while still providing a good dark matter candidate and gauge coupling unification. Here, we study the effects of PGM if the input boundary conditions for soft supersymmetry breaking masses are pushed beyond the unification scale and higher dimensional operators are included. The added running beyond the unification scale opens up the parameter space by relaxing the constraints on tan beta . If higher dimensional operators involving the SU(5) adjoint Higgs are included, the mass of the heavy gauge bosons of SU(5) can be suppressed leading to proton decay, prightarrow pi ^0 e^+, that is within reach of future experiments. Higher dimensional operators involving the supersymmetry breaking field can generate additional contributions to the A- and B-terms of order m_{3/2}. The threshold effects involving these A- and B-terms significantly impact the masses of the gauginos and can lead to a bino LSP. In some regions of parameter space the bino can be degenerate with the wino or gluino and give an acceptable dark matter relic density.

Fits to non-supersymmetric SO(10) models with type I and II seesaw mechanisms using renormalization group evolution

We consider numerical fits to non-supersymmetric SO(10)-based models in which neutrino mass is generated by the type-I or type-II seesaw mechanism or a combination of both. The fits are performed with a sophisticated top-down procedure, taking into account the renormalization group equations of the gauge and Yukawa couplings, integrating out relevant degrees of freedom at their corresponding mass scales, and using recent data for the Standard Model observables. We find acceptable fits for normal neutrino mass ordering only and with neutrino mass generated by either type-I seesaw only or a combination of types I and II seesaw in which type-I seesaw is dominant. Furthermore, we find predictions from the best fit regarding the small neutrino masses, the effective neutrinoless double beta decay mass, and the leptonic CP-violating phase. Finally, we show that the fits are rather insensitive to the chosen value of the unification scale.

Rparity from string compactification

In this paper, we embed the $\Z_{4R}$ parity as a discrete subgroup of a global symmetry \UoR\,obtained from $\Z_{12-I}$ compactification of heterotic string $\EE8$. A part of \UoR\,transformation is the shift of the anticommuting variable $\vartheta$ to $e^{i\alpha}\vartheta$ which necessarily incoorporate the transformation of internal space coordinate. Out of six internal spaces, we identify three U(1)'s whose charges are denoted as $Q_{18},Q_{20}$, and $Q_{22}$. The \UoR~is defined as \UEE$\times$\UKK~where \UEE~is the part from $\EE8$ and \UKK~is the part generated by $Q_{18},Q_{20}$, and $Q_{22}$. We propose a method to define a \UoR~direction. The needed vacuum expectation values for breaking gauge U(1)'s except U(1)$_Y$ of the standard model carry \UoR~charge 4 modulo 4 such that \UoR~is broken down to $\Z_{4R}$ at the grand unification scale. $\Z_{4R}$ is broken to $\Z_{2R}$ between the intermediate ($\sim 10^{11\,}\gev$) and the electroweak scales ($100\,\gev\sim 1\,\tev$). The conditions we impose are proton longevity, a large top quark mass, and acceptable magnitudes for the $\mu$ term and neutrino masses.